To understand earth formations and how such formations behave, it is necessary to determine the permittivity of the rock comprising the formation. For example, in order to produce hydrocarbons economically, a reasonably accurate estimation of hydrocarbon volume and mobility needs to be performed. The measurement of dielectric constant (or dielectric permittivity) of formations surrounding a borehole is known to provide useful information about the formations for hydrocarbon transport purposes. The dielectric constant of the different materials in earth formations vary widely—for example, dielectric constants are roughly 2.2 for oil, 7.5 for limestone, and 80 for water—so measurement of dielectric properties can be a useful means of formation evaluation.
For hydrocarbon production purposes, effective measurement of formation permittivity and/or conductivity must be performed. The earth formation consists of the rock matrix and the pore fluids—usually hydrocarbon and water—that are present in and/or may pass through the pores in the rock matrix. In order to deduce the volumetric fraction of water in the formation from the effective permittivity of the formation, a relationship between the properties of the constituents of the formation and the mixture of the constituents (known as a “mixing rule”) is generally used. Among several existing dielectric mixing rules, the Complex Refractive Index Method (“CRIM”) is one of the most widely used. A disadvantage of mixing rules is that they require knowledge of both the matrix and fluid complex permittivity, which knowledge may be difficult to ascertain.
For purposes of this application, a rock will be regarded as including a porous and permeable solid mineral matrix, comprising for example sandstone or carbonate grains. Previously, the permittivity of such a rock has been measured when saturated with a fluid that occupies the pores of the rock. However, obtaining solely the rock matrix permittivity—often termed the “dry rock permittivity”—from such measurements on saturated rock is problematic because of the contribution of the pore space in the rock to the rock matrix permittivity; which contribution cannot be determined from the saturated rock measurement. A similar problem applies to obtaining the permittivity of the rock matrix from permittivity measurements made on a powdered sample of the rock, e.g. in a measurement system where the grains of the powdered rock sample are suspended in a liquid or gaseous dielectric; the problem arising again from the fact that the permittivity effects of the pore space in the rock matrix cannot be measured from the saturated powder as the fluid saturating the pores mixes the effect of the pores with the measured permittivity.
As discussed above, calculating the permittivity of a rock core or a powder sampled from a formation requires the use of mixture rules that relate the permittivity of a mixture of rock and liquid in a sample to the individual permittivities of the solid and the liquid components of the sample. Mixture rules use the permittivities of the components of the mixture and the volume fraction of each of the components in the mixture as parameters. However, the mixture rules are of unknown validity and can differ markedly from one another, and hence can produce large errors in rock matrix permittivity values that are derived from saturated rock permittivity measurements.